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• About
• Status
• Related packages
• Installation
• Dependencies
• Usage examples
• API
  • Constants
  • Matrix creation
    • WebGL related
  • Matrix conversion
  • Setters
  • Row & column accessors
  • Componentwise matrix - matrix
  • Componentwise matrix - scalar
  • Matrix multiplication
  • Matrix - vector multiplication
  • Determinant & inversion
  • Matrix transposition
  • Quaternion
• Authors
• License

About

Matrix & quaternion operations for 2D/3D geometry processing.

This package provides 160+ matrix & quaternion operations for 2D/3D geometry processing and acts as companion package for @thi.ng/vectors. Like with the vectors package, most functions are defined as multi-method dispatching to optimized implementations based on matrix size (which themselves are exposed for direct use too).

Any ArrayLike type can be used as matrix containers (e.g. JS arrays, typed arrays, custom impls) and hence many other functions provided by the vectors package can also be used directly with matrices (where sensible).

Status

STABLE - used in production

Search or submit any issues for this package

Related packages

• @thi.ng/color - Array-based color types, CSS parsing, conversions, transformations, declarative theme generation, gradients, presets
• @thi.ng/geom - Functional, polymorphic API for 2D geometry types & SVG generation
• @thi.ng/vector-pools - Data structures for managing & working with strided, memory mapped vectors
• @thi.ng/vectors - Optimized 2d/3d/4d and arbitrary length vector operations, support for memory mapping/layouts

Installation

yarn add @thi.ng/matrices

ESM import:

import * as mat from "@thi.ng/matrices";

Browser ESM import:

<script type="module" src="https://esm.run/@thi.ng/matrices"></script>

JSDelivr documentation

For Node.js REPL:

const mat = await import("@thi.ng/matrices");

Package sizes (brotli'd, pre-treeshake): ESM: 5.19 KB

Dependencies

• @thi.ng/api
• @thi.ng/checks
• @thi.ng/math
• @thi.ng/vectors

Note: @thi.ng/api is in most cases a type-only import (not used at runtime)

Usage examples

17 projects in this repo's /examples directory are using this package:

Screenshot	Description	Live demo	Source
	(Re)Constructing the thi.ng logo using a 2D signed-distance field	Demo	Source
	Augmenting thi.ng/geom shapes for WebGL, using instancing & attribute buffers	Demo	Source
	Converting thi.ng/geom shape types for WebGL	Demo	Source
	Various hdom-canvas shape drawing examples & SVG conversion / export	Demo	Source
	Barnsley fern IFS fractal renderer	Demo	Source
	Live coding playground for 2D geometry generation using @thi.ng/pointfree-lang	Demo	Source
	2D scenegraph & shape picking	Demo	Source
	2D scenegraph & image map based geometry manipulation	Demo	Source
	Minimal shader graph developed during livestream #2	Demo	Source
	Fitting, transforming & plotting 10k data points per frame using SIMD	Demo	Source
	Entity Component System w/ 100k 3D particles	Demo	Source
	3D wireframe textmode demo	Demo	Source
	Visual comparison of biased vs. unbiased normal vectors projected on the surface of a sphere	Demo	Source
	WebGL multi-colored cube mesh	Demo	Source
	WebGL cube maps with async texture loading	Demo	Source
	WebGL instancing, animated grid	Demo	Source
	WebGL MSDF text rendering & particle system	Demo	Source

API

Generated API docs

Constants

• IDENT22 / IDENT23 / IDENT33 / IDENT44

Matrix creation

• fit23 / fit44
• rotation22 / rotation23
• rotationAroundAxis33 / rotationAroundAxis44
• rotationAroundPoint23
• rotationX33 / rotationX44
• rotationY33 / rotationY44
• rotationZ33 / rotationZ44
• scale22 / scale23 / scale33 / scale44
• scaleWithCenter23 / scaleWithCenter44
• shearX22 / shearY22
• shearX23 / shearY23
• shearXY33 / shearXZ33 / shearYX33 / shearYZ33 / shearZX33 / shearZY33
• shearXY44 / shearXZ44 / shearYX44 / shearYZ44 / shearZX44 / shearZY44
• skewX22 / skewY22
• skewX23 / skewY23
• skewXY33 / skewXZ33 / skewYX33 / skewYZ33 / skewZX33 / skewZY33
• skewXY44 / skewXZ44 / skewYX44 / skewYZ44 / skewZX44 / skewZY44
• translation23 / translation44
• transform23 / transform44

WebGL related

• frustum / frustumBounds
• lookAt
• ortho
• perspective
• viewport

Matrix conversion

• mat22to23
• mat23to22 / mat23to44
• mat33to44 / mat44to33
• normal44

Setters

• set / set22 / set23 / set33 / set44
• identity / identity22 / identity23 / identity33 / identity44

Row & column accessors

• column / column22 / column23 / column33 / column44
• row / row22 / row23 / row33 / row44

Componentwise matrix - matrix

• add / add22 / add23 / add33 / add44
• div / div22 / div23 / div33 / div44
• mul / mul22 / mul23 / mul33 / mul44
• sub / sub22 / sub23 / sub33 / sub44

Componentwise matrix - scalar

• addN / addN22 / addN23 / addN33 / addN44
• divN / divN22 / divN23 / divN33 / divN44
• mulN / mulN22 / mulN23 / mulN33 / mulN44
• subN / subN22 / subN23 / subN33 / subN44

Matrix multiplication

• mulM / mulM22 / mulM23 / mulM33 / mulM44
• concat

Matrix - vector multiplication

• mulV / mulV22 / mulV23 / mulV33 / mulV344 / mulV44
• project
• unproject

Determinant & inversion

• det22 / det23 / det33 / det44
• det44FromCoeffs / detCoeffs44
• diag / diag22 / diag23 / diag33 / diag44
• invert / invert22 / invert23 / invert33 / invert44
• trace

Matrix transposition

• transpose22 / transpose33 / transpose44

Quaternion

• alignmentQuat
• conjugateQ
• invertQ
• mixQ
• mulQ
• mulVQ
• quatFromAxisAngle
• quatFromEuler
• quatToAxisAngle
• quatToMat33
• quatToMat44

Authors

• Karsten Schmidt

If this project contributes to an academic publication, please cite it as:

@misc{thing-matrices,
  title = "@thi.ng/matrices",
  author = "Karsten Schmidt",
  note = "https://thi.ng/matrices",
  year = 2018
}

License

© 2018 - 2025 Karsten Schmidt // Apache License 2.0